© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 3681wileyonlinelibrary.com

CO

MM

UN

ICATIO

N

Simultaneous Enhancement of Electrical Conductivity and Thermopower of Bi 2 Te 3 by Multifunctionality of Native Defects

Joonki Suh , Kin Man Yu , Deyi Fu , Xinyu Liu , Fan Yang , Jin Fan , David J. Smith , Yong-Hang Zhang , Jacek K. Furdyna , Chris Dames , Wladyslaw Walukiewicz , and Junqiao Wu *

J. Suh, Dr. K. M. Yu, Dr. D. Fu, Dr. W. Walukiewicz, Prof. J. Wu Department of Materials Science and Engineering University of California Berkeley , CA 94720 , USA E-mail: wuj@berkeley.edu J. Suh, Dr. K. M. Yu, Dr. D. Fu, Dr. W. Walukiewicz, Prof. J. Wu Materials Sciences Division Lawrence Berkeley National Laboratory Berkeley , CA 94720 , USA Dr. X. Liu, Prof. J. K. Furdyna Department of Physics University of Notre Dame Notre Dame , IN 46556 , USA Dr. F. Yang, Prof. C. Dames Department of Mechanical Engineering University of California Berkeley , CA 94720 , USA Dr. J. Fan, Prof. D. J. Smith Department of Physics Arizona State University Tempe , AZ 85287 , USA Prof. Y.-H. Zhang School of Electrical Computer and Energy Engineering Arizona State University Tempe , AZ 85287 , USA

DOI: 10.1002/adma.201501350

temperature thermoelectrics are Bi 2 Te 3 -based bulk alloys, and their best ZT is still around 1, e.g., n-type Bi 2 Te 2.7 Se 0.3 with ZT max ≈0.9 [ 6 ] and p-type Bi 0.5 Sb 1.5 Te 3 with ZT max ≈1.2. [ 7 ] The approach of phonon engineering has limited potential for these materials as their thermal conductivity is already low and does not have much room for further reduction. [ 5,8 ] Hence, it is ultimately necessary to seek a breakthrough in materials engineering that would improve ZT beyond what is limited by the trade-off between α and σ , preferably with a single meth-odology. Though various experimental (e.g., energy fi ltering in Bi 2 Te 3 /Bi 2 Se 3 superlattices) [ 9 ] and theoretical (e.g., hybridi-zation by topological surface states) [ 10 ] approaches have been attempted or proposed, only α or σ , but not both, is effectively improved in these cases. The trade-off between α and σ origi-nates fundamentally from the fact that a high α prefers a large asymmetry in electron population above and below the Fermi level, thus a rapid variation in the material density of states; this is opposite to the direction of increasing σ and n , which occurs typically as the Fermi level is displaced deep into the band where the density of states is relatively constant.

Here, we demonstrate a new way to drastically enhance thermoelectric properties of Bi 2 Te 3 by utilizing native defects (NDs). We present a new, atomic-scale mechanism to break the trade-off between α and σ , simultaneously improving both for enhanced ZT. Such a unique combination of electrical and thermoelectric benefi ts originates from the multifunction-ality of native point defects in Bi 2 Te 3 acting as electron donors and electron energy fi lters. The presented results establish the importance of understanding and controlling point defects in thermoelectric materials as a venue to much improve their device performance.

Bi 2 Te 3 thin fi lms with a wide range of thicknesses (11 nm to 1 µm) were grown by molecular beam epitaxy (MBE) on semi-insulating GaAs (001) substrates. In Figure 1 a, the cross-section high-resolution transmission electron microscopy (HRTEM) image shows clean interfaces without amorphous phases, and shows highly parallel quintuple layers (QLs). The crystallinity of the MBE fi lms was further evaluated by X-ray diffraction (XRD) using the Cu Kα1 radiation line (Figure 1 b). The XRD pattern clearly shows strong refl ections from {003}-type lattice planes. This is a strong indication of the highly c -axis directional growth of the MBE fi lms. The QL thickness was calculated from the XRD data, giving d QL = 1.014 ± 0.005 nm for Bi 2 Te 3 that is consistent with the value of 1.016 nm for bulk Bi 2 Te 3 . [ 11 ]

Thermoelectric materials have been heavily investigated over the past several decades for environment-friendly applications of solid-state energy conversion: heat to electricity and vice versa. [ 1,2 ] The fi gure of merit (ZT) of thermoelectric materials is given by α 2 σT / κ , in which α is the Seebeck coeffi cient (ther-mopower), σ is the electrical conductivity, T is absolute tem-perature, and κ is the thermal conductivity. Since α and σ are anticorrelated through the free carrier concentration ( n ), recent successes to enhance ZT have mostly relied on reduction of lat-tice thermal conductivity ( κ l ) without signifi cantly affecting the power factor ( α 2 σ ). [ 3 ] This approach has achieved ZT of PbTe–SrTe compounds exceeding 2 at temperatures above 900 K by effectively scattering acoustic phonons with all-length-scale mean free paths. [ 4 ]

On the contrary, the best single-phase materials (i.e., excluding superlattices) [ 5 ] available today for near-room-

Adv. Mater. 2015, 27, 3681–3686

www.advmat.dewww.MaterialsViews.com

3682 wileyonlinelibrary.com © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

CO

MM

UN

ICATI

ON

Hall effect measurements were performed in the van der Pauw confi guration using an Ecopia HMS-3000 system. As presented in Figure 1 c, n decreases and carrier mobility ( µ ) increases monotonically with fi lm thickness, and tends to saturate in thicker fi lms, akin to those observed in Bi 2 Se 3 MBE thin fi lms. [ 12 ] In order to generate NDs, the samples were irra-diated with 3 MeV alpha particles (He 2+ ) with doses ranging from 2 × 10 13 to 3 × 10 15 cm −2 . The projected range of these particles exceeds 8 µm in Bi 2 Te 3 , as calculated by Monte Carlo simulation using the stopping and range of ions in matter (SRIM) program (Figure S1, Supporting Information, inset). Therefore, the He 2+ ions completely pass through the entire fi lm thickness, leaving behind NDs that are uniformly distributed in both lateral and depth directions. As pre-dicted by SRIM, the primary NDs induced by irradiation are Bi (V Bi ) and Te (V Te ) vacan-cies and corresponding interstitials with average densities of 1.2 × 10 4 (for Bi) and 1.8 × 10 4 cm −3 /ion cm −2 (for Te), respec-tively, that scale linearly with the irradiation dose (Figure 1 d). We note that within the doses used, the materials are gently dam-aged with only point defects generated; no extended defects, surface sputtering,

non-stoichiometry, or amorphization is observed. [ 13 ] We also note that the substrate (semi-insulating GaAs) does not contribute to the electrical conductivity measured from the fi lm. It is theoretically expected [ 14 ] and experimentally confi rmed that the substrate remains electrically extremely insulating after the irradiation, with a sheet resistance orders of magnitude higher than that of the fi lm.

After the irradiation, σ of the Bi 2 Te 3 increases for fi lms with thickness between 47 and 740 nm, and this trend is more sig-nifi cant for thicker fi lms ( Figure 2 a). Con-sidering the multiple conduction chan-nels (e.g., surface and bulk) in Bi 2 Te 3 , this effect suggests that bulk transport, which is affected by the NDs, plays an important role in the electrical conductance in this thick-ness range. In contrast, very thin fi lms are insensitive to irradiation, because surface conduction dominates and remains robust to irradiation. Hall effect measurements reveal that the enhanced σ is a combined effect of a monotonic increase in n and a non-monotonic change of µ (Figure 2 b,c). The increase in n indicates that the irra-diation predominantly introduces donor-like NDs, which are also considered as the pri-mary reason for the unintentional n-type behavior of as-prepared Bi 2 Te 3 . [ 15,16 ]

As shown in Figure 2 c, the mobility of thick fi lms increases remarkably (by up to 50%) upon irradiation until an intermediate dose (≈2 × 10 14 cm −2 ), then steadily decreases. For

Adv. Mater. 2015, 27, 3681–3686

www.advmat.dewww.MaterialsViews.com

Figure 1. Characterization of pristine Bi 2 Te 3 fi lms. a) Cross-sectional HRTEM image and b) XRD data of Bi 2 Te 3 fi lms grown by MBE on a GaAs (001) substrate. c) Hall effect determined carrier density and mobility as a function of thickness at room temperature. d) The concentra-tion of vacancies was calculated using SRIM for 740 nm thick Bi 2 Te 3 fi lm under 3 MeV alpha particles irradiation. SRIM predicts that the concentration of irradiation-induced defects is very uniform along the depth of fi lms. As indicated by the units (cm −3 /cm −2 ), the real vacancy con-centration is given by this value multiplied with the irradiation dose (in units cm −2 ), implying a linear dependence between them.

Figure 2. Electrical transport of ND-engineered Bi 2 Te 3 thin fi lms. a) Electrical conductivity variation upon irradiation of fi lms with different thicknesses. b) Electron concentration and c) electron mobility of representative Bi 2 Te 3 fi lms as a function of irradiation dose, determined by Hall effect measurement at room temperature.

3683wileyonlinelibrary.com© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

CO

MM

UN

ICATIO

N

conventional semiconductors, it is believed that NDs produced by irradiation are charged Coulomb scattering centers, low-ering the carrier relaxation time and thus the carrier mobility. Recent theoretical and experimental studies have shown that in addition to the bulk transport, Bi 2 Te 3 exhibits signifi cant surface or grain boundary transport, which are attributed to the topological insulator state [ 17 ] or to a surface accumulation layer. [ 18,19 ] We propose that the irradiation-induced NDs cause the unusual mobility behavior of Figure 2 c by modifying the relative contribution of conduction electrons between the bulk and the surface (including grain boundaries and specimen sur-face). Simplifying the system into two electrically conduction channels, surface and bulk, we modeled the dependence of carrier concentration and mobility on irradiation dose. [ 20,21 ] As illustrated in the inset of Figure 3 a, parallel electron transport was considered in the surface and bulk layers. With the relative contribution from each layer, effective (modeled) electron con-centration ( n *) and mobility ( µ* ) were determined using:

n

n d d n d d

n d d n d d

( / ) ( / )

( / ) ( / )* s s s b b b

2

s s2

s b b2

b

μ μμ μ

[ ]=

++

(1)

n d d n d d

n d d n d d

( / ) ( / )

( / ) ( / )* s s

2s b b

2b

s s s b b b

μμ μμ μ

=++

(2)

where n s ( n b ) and µ s ( µ b ) are the electron concentration and mobility of surface (bulk) layer, respectively, and d s ( d b ) is the thickness of surface (bulk) layer, and the total thickness, d , is given by s bd d d= + . [ 20 ] The surface properties ( n s and µ s ) are inferred from Hall effect data of very thin fi lms (11–22 nm) where surface contribution is dominant. Note that in this model n s and µ s are assumed to be not strongly affected by irradiation, i.e., the irradiation generates more free electrons only in the bulk (increasing net n b ), as opposed to redistributing existing surface n s to the bulk n b . Indeed, in very thin fi lms where the bulk conduction is insignifi cant, the measured n* (Hall µ* ) is always dominated by n s ( µ s ), staying high (low) and nearly intact upon irradiation (Figure 2 b,c). Given that µ s is insensi-tive to the irradiation and µ s « µ b , [ 13,22 ] n * and µ * were fi tted to

the experimental Hall effect data at various irradiation doses. Such a bilayer model is in good agreement with the experi-mental data for fi lms with various thicknesses, explaining both the monotonically increasing n* and, in particular, non-mono-tonic variation of µ* upon irradiation (see representative fi tting in Figure 3 ). The irradiation-induced, drastic net increase in bulk electron density would shift the weight more toward bulk conduction, compared to the case in pristine fi lms where sur-face conduction weighs more. Therefore, although µ b slightly decreases upon irradiation, the measured µ * shows an increase at intermediate irradiation doses, because after irradiation the higher-mobility bulk conduction plays a much more signifi cant role than the surface conduction.

More importantly, while steadily increasing σ , the NDs at intermediate irradiation doses also improve the thermopower ( α ) of the thick Bi 2 Te 3 fi lms as seen in Figure 4 a. This simulta-neous enhancement of α and σ is unusual, since in most cases α decreases and σ increases with increasing n . Normally, as n increases, the Fermi level ε F moves deeper into the band where the density of states is fl atter, hence reducing the entropy car-ried by charges around ε F . [ 23 ] The simultaneous enhancement of α and σ is observed only in relatively thicker fi lms (>47 nm), which suggests that the measured thermopower is dominated by the bulk contribution that can be tailored by the NDs.

In the relaxation time model, the thermopower in the degen-erate doping limit is given by:

3

3

2B

2B

F

k

e

k Trα π

ε≈ ⋅ ⋅ ⋅ +⎛

⎝⎜⎞⎠⎟

(3)

where r is the index of the electron relaxation time related to kinetic energy, ( ) rτ ε ε∝ , [ 24 ] and ε F is measured from the con-duction band edge. Equation ( 3) not only predicts the ordinary decrease in α as n increases (through ε F ), but also an increase in α when r increases. The former leads to the conventional wisdom of the inverse coupling between α and σ , while the latter allows it to be broken, as in our case. It is known that r varies from −1/2 for acoustic phonon scattering to 3/2 for ion-ized impurity scattering. [ 24 ] As shown in Figure 4 b, in pristine

Adv. Mater. 2015, 27, 3681–3686

www.advmat.dewww.MaterialsViews.com

Figure 3. Bilayer Hall effect modeling of Bi 2 Te 3 fi lms. Comparison of a) electron concentration and b) electron mobility between experimental data with bilayer modeled data for 240 nm fi lm. Inset shows schematics of the two conduction channels of surface and bulk. Surface properties are assumed to be constant for all the fi lms within the ranges of thickness and irradiation dose. Also, its thickness ( d s ) is assumed to be ≈3 nm, considering other contributions such as grain boundaries in the bulk as well as the surface roughness.

3684 wileyonlinelibrary.com © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

CO

MM

UN

ICATI

ON

fi lms, the measured α as a function of n follows the trend with calculation using r = −1/2, indicating that electrons are mostly scattered by phonons in these fi lms. This is consistent with theoretical prediction that electrical transport in Bi 2 Te 3 at similar carrier concentrations (≈1 × 10 19 cm −3 ) is limited by phonon scattering, [ 25 ] and is indeed reasonable considering its very large dielectric constant ( ε s = 290). [ 26 ] However, the high density and multiple charge states of NDs introduced by irradiation as ionized impurities cause a transition of the scat-tering mechanism from phonon-dominated ( r = −1/2) toward more impurity-dominated ( r = 3/2); as a result, the thermo-power is drastically enhanced, as indicated by the arrows in Figure 4 b. For the irradiated fi lms, α starts to follow the cal-culated trend with r = 3/2. This transition is also confi rmed by the fact that the mobility µ of the pristine fi lm becomes much higher when measured at low temperatures, while µ is less temperature-sensitive for irradiated fi lms (Figure S1, Sup-porting Information).

The ND-enabled decoupling of α and σ naturally leads to a signifi cant increase in the thermoelectric power factor, α 2 σ , as shown in Figure 4 c. It reaches a peak value of 3.4 ± 0.3 mW m −1 K −2 for the 740 nm fi lm at an irradiation dose of 4 × 10 14 cm −2 , representing an eightfold enhancement from its pristine value. This peak power factor is a factor of 1.5–3 higher compared to recently reported values in binary Bi 2 Te 3 . [ 9,27 ]

In addition, the effect of the NDs on the cross-plane ( c -axis) thermal conductivity ( κ ⊥ ), particularly in the thick Bi 2 Te 3 fi lms, was investigated using the differential 3 ω technique. [ 28 ] We found that κ ⊥ decreases by up to 35% upon the irradia-tion as shown in Figure 5 . It is noteworthy that the reduction in κ ⊥ is substantially stronger than the case if the NDs were replaced by conventional donor ions at the same concentra-tions (≈3 × 10 19 cm −3 , or ≈0.1% of the atomic sites). This is because a point defect’s ability to scatter acoustic phonons goes as the square of the defect’s relative deviation in mass, radius, and/or bonding strength. [ 29 ] These relative deviations are much stronger for the irradiation-introduced NDs (vacan-cies, antisites, and missing bonds) as compared to simple

substitutional dopants. [ 30 ] As our measured κ is cross-plane (⊥), while the measured α and σ are in-plane (//), a rigorous evalua-tion of ZT is not within the scope of this work due to the aniso-tropic transport. However, given the eightfold enhancement in α 2 σ , it is safe to conclude that ZT is expected to be signifi cantly enhanced accordingly, because κ is expected to only decrease upon the irradiation.

To summarize, irradiation-induced NDs drastically enhance thermoelectric properties in Bi 2 Te 3 by decoupling the three key thermoelectric parameters and simultaneously modi-fying all of them toward the desired direction. This is ena-bled by the multiple functionality of the NDs acting benefi -cially as electron donors, energy-dependent charge scattering centers, and phonon blockers. Our results suggest that a sig-nifi cant improvement of the thermoelectric performance can

Adv. Mater. 2015, 27, 3681–3686

www.advmat.dewww.MaterialsViews.com

Figure 5. Cross-plane thermal conductivity of the 740 nm Bi 2 Te 3 fi lm upon irradiation. Inset illustrates the in-plane and cross-plane confi gura-tion of the textured fi lm.

Figure 4. Enhancement of Seebeck coeffi cient and power factor by the NDs. a) Variation of α upon irradiation. b) α enhancement of irradiated Bi 2 Te 3 fi lms in the thick fi lm regime (Pisarenko plot). The dotted lines show the results of calculated Seebeck coeffi cient with different scattering time index r ranging from phonon-scattering (−1/2) to ionized impurity scattering (3/2). Here, the rigorous Fermi–Dirac carrier statistics are used such that the calculation is valid across all concentrations ranging from non-degenerate to degenerate. The arrow indicates simultaneous increase of α and carrier concentration ( n ) of the fi lms. c) Thermoelectric power factor enhancement in the ND-engineered Bi 2 Te 3 fi lms.

3685wileyonlinelibrary.com© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

CO

MM

UN

ICATIO

N

be achieved through a judicious control of the ND species and their density by post-growth processing with high-energy beams. As the NDs are expected to be generated and behave in the similar way in a wide range of narrow-bandgap semi-conductors (e.g., observed in InN and InAs) [31,32] it is possible to extend this method to improve the fi gure of merit of other materials in conjunction with other widely utilized techniques such as alloying and nano- and hetero-structuring. Although irradiation cannot be directly applied to bulk materials due to limitation in irradiation projection range (≈10 µm), our approach is of practical importance because thin fi lm thermo-electrics could play an important role in on-chip cooling; [ 33 ] in addition, our approach can be used in complementary to existing nanotechnology to scale up in bulk thermoelectrics. For instance, nano-objects (such as Bi 2 Te 3 nanowires, particles, and nanoplates) can be irradiated, and then pressed into bulk or assembled into bulk using a polymer matrix, as demon-strated by Coates et al. [ 34 ]

Experimental Section Thin-Film Growth : The Bi 2 Te 3 thin fi lms were grown using a dual

chamber Riber 32 solid-source MBE system. The Bi and Te 2 fl uxes were generated by standard effusion cells, and the structure and thickness of the fi lms were monitored in situ by refl ection high-energy electron diffraction. The growth step was initiated by heating an epi-ready semi-insulating GaAs (001) substrate to 600 °C for de-oxidation in the III-V MBE chamber. This was followed by deposition of a 100 nm GaAs buffer layer. This modifi ed substrate was then transferred to the chalcogenide MBE chamber through an ultra-high vacuum connection. The growth of the MBE fi lm was initiated by the deposition of a series of monolayers of Te–Bi–Te–Bi–Te (a QL) in atomic layer epitaxy fashion at room temperature. The substrate was then gradually heated to 300 °C, and the MBE growth of Bi 2 Te 3 was subsequently performed under Te-rich condition of T Te (250 °C) < T substrate (300 °C) < T Bi (≈500 °C) with a Te:Bi beam equivalent pressure ratio ranging from 20:1 to 80:1. The fi lms were grown layer by layer, with typical growth rates of 0.5–2 QL min −1 . Later, the compositions and thicknesses of the fi lms were confi rmed by Rutherford backscattering spectroscopy (RBS) before further experiments.

Alpha Particle Irradiation : The pristine samples were irradiated in an accumulated manner employing a high-energy (3 MeV) He 2+ beam with current between 35 and 100 nA generated by an NEC Pelletron tandem accelerator. The accumulated dose was monitored by measuring the total charge on the sample in an electrically isolated irradiation chamber. The ion beam was defocused to an area of 40 mm 2 maintaining a homogeneous ion fl uence over the entire fi lm, assuring the introduction of uniformly distributed NDs, both vertically and laterally.

Thermoelectric Transport Characterization : Electrical transport was measured by Hall effect using an Ecopia HMS-3000 system at room temperature. Seebeck coeffi cient was measured by a home-built thermopower measurement system. A differential 3 ω technique was used to measure the cross-sectional thermal conductivity ( κ ⊥ ) of the ND-engineered Bi 2 Te 3 thin fi lm with a thickness of 740 nm at various irradiation doses. Using the plasma-enhanced chemical vapor deposition (PECVD) technique, a 500 nm SiO 2 layer was simultaneously deposited on the top of both a pristine Bi 2 Te 3 thin fi lm, for electrical isolation, and a reference (identical semi-insulating GaAs (001)) bare substrate at 300 °C. Two identical 20 µm × 1500 µm gold line heaters were then patterned on the top of PECVD-grown SiO 2 layers using conventional photolithography. Since the thicknesses of the dielectric layer (500 nm) and Bi 2 Te 3 fi lm (740 nm) are much thinner than the width of the patterned gold heater (20 µm), the through-thickness (along c -axis) heat conduction can be approximated as 1D to better than 5% accuracy. [ 35 ]

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements This work was supported by a NSF CAREER Award under Grant No. DMR-1055938. The irradiation and Hall effect parts were supported by the Offi ce of Science, Offi ce of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The fi lm growth of Bi 2 Te 3 thin fi lms were supported by NSF Grant No. DMR10-05851, NSF Grant No. ECCS10-02114, and an AFOSR Grant No. FA9550-10-1-0129. The authors acknowledge use of facilities in the John M. Cowley Center for High Resolution Electron Microscopy at Arizona State University. The authors wish to thank Prof. Renkun Chen, Prof. Jae Hun Seol, Sean Lubner, Jason Chee, and Chun-Hao Huang for valuable discussions and technical support.

Received: March 20, 2015 Revised: April 20, 2015

Published online: May 12, 2015

[1] S. Chu , A. Majumdar , Nature 2012 , 488 , 294 . [2] C. J. Vineis , A. Shakouri , A. Majumdar , M. G. Kanatzidis , Adv. Mater.

2010 , 22 , 3970 . [3] A. Shakouri , Annu. Rev. Mater. Res. 2011 , 41 , 399 . [4] K. Biswas , J. He , I. D. Blum , C.-I. Wu , T. P. Hogan , D. N. Seidman ,

V. P. Dravid , M. G. Kanatzidis , Nature 2012 , 489 , 414 . [5] R. Venkatasubramanian , E. Siivola , T. Colpitts , B. O’Quinn , Nature

2001 , 413 , 597 . [6] X. Yan , B. Poudel , Y. Ma , W. S. Liu , G. Joshi , H. Wang , Y. Lan ,

D. Wang , G. Chen , Z. F. Ren , Nano Lett. 2010 , 10 , 3373 . [7] B. Poudel , Q. Hao , Y. Ma , Y. Lan , A. Minnich , B. Yu , X. Yan ,

D. Wang , A. Muto , D. Vashaee , X. Chen , J. Liu , M. S. Dresselhaus , G. Chen , Z. Ren , Science 2008 , 320 , 634 .

[8] J. P. Fleurial , L. Gailliard , R. Triboulet , H. Scherrer , S. Scherrer , J. Phys. Chem. Sol. 1988 , 49 , 1237 .

[9] Y. Min , J. W. Roh , H. Yang , M. Park , S. I. Kim , S. Hwang , S. M. Lee , K. H. Lee , U. Jeong , Adv. Mater. 2013 , 25 , 1425 .

[10] P. Ghaemi , R. S. K. Mong , J. E. Moore , Phys. Rev. Lett. 2010 , 105 , 166603 .

[11] J. O. Jenkins , J. A. Rayne , R. W. Ure , Phys. Rev. B 1972 , 5 , 3171 .

[12] Y. S. Kim , M. Brahlek , N. Bansal , E. Edrey , G. A. Kapilevich , K. Iida , M. Tanimura , Y. Horibe , S.-W. Cheong , S. Oh , Phys. Rev. B 2011 , 84 , 073109 .

[13] J. Suh , D. Fu , X. Liu , J. K. Furdyna , K. M. Yu , W. Walukiewicz , J. Wu , Phys. Rev. B 2014 , 89 , 115307 .

[14] W. Walukiewicz , Phys. Rev. B 1988 , 37 , 4760 . [15] D. O. Scanlon , P. D. C. King , R. P. Singh , A. de la Torre ,

S. M. Walker , G. Balakrishnan , F. Baumberger , C. R. A. Catlow , Adv. Mater. 2012 , 24 , 2154 .

[16] D. West , Y. Y. Sun , H. Wang , J. Bang , S. B. Zhang , Phys. Rev. B 2012 , 86 , 121201(R) .

[17] Y. L. Chen , J. G. Analytis , J.-H. Chu , Z. K. Liu , S.-K. Mo , X. L. Qi , H. J. Zhang , D. H. Lu , X. Dai , Z. Fang , S. C. Zhang , I. R. Fisher , Z. Hussain , Z.-X. Shen , Science 2009 , 325 , 178 .

[18] C. Chen , S. He , H. Weng , W. Zhang , L. Zhao , H. Liu , X. Jia , D. Mou , S. Liu , J. He , Y. Peng , Y. Feng , Z. Xie , G. Liu , X. Dong , J. Zhang , X. Wang , Q. Peng , Z. Wang , S. Zhang , F. Yang , C. Chen , Z. Xu ,

Adv. Mater. 2015, 27, 3681–3686

www.advmat.dewww.MaterialsViews.com

3686 wileyonlinelibrary.com © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

CO

MM

UN

ICATI

ON

Adv. Mater. 2015, 27, 3681–3686

www.advmat.dewww.MaterialsViews.com

X. Dai , Z. Fang , X. J. Zhou , Proc. Natl. Acad. Sci. USA 2012 , 109 , 3694 .

[19] M. S. Bahramy , P. D. C. King , A. de la Torre , J. Chang , M. Shi , L. Patthey , G. Balakrishnan , Ph. Hofmann , R. Arita , N. Nagaosa , F. Baumberger , Nat. Commun. 2012 , 3 , 1159 .

[20] R. L. Petritz , Phys. Rev. 1958 , 110 , 1254 . [21] R. E. Jones , K. M. Yu , S. X. Li , W. Walukiewicz , J. W. Ager ,

E. E. Haller , H. Lu , W. J. Schaff , Phys. Rev. Lett. 2006 , 96 , 125505 . [22] N. P. Butch , K. Kirshenbaum , P. Syers , A. B. Sushkov , G. S. Jenkins ,

H. D. Drew , J. Paglione , Phys. Rev. B 2010 , 81 , 241301 . [23] H. J. Goldsmid , Introduction to Thermoelectricity , Springer , Heidel-

berg, Germany 2010 . [24] F. D. Rosi , Solid-State Electron. 1968 , 11 , 833 . [25] B.-L. Huang , M. Kaviany , Phys. Rev. B 2008 , 77 , 125209 . [26] W. Richter , H. Kohler , C. R. Becker , Phys. Status Solidi B 1977 , 84 , 619 . [27] L. Hu , H. Gao , X. Liu , H. Xie , J. Shen , T. Zhu , X. Zhao , J. Mater.

Chem. 2012 , 22 , 16484 .

[28] C. Dames , G. Chen , Rev. Sci. Instrum. 2005 , 76 , 124902 . [29] P. G. Klemens , Proc. Phys. Soc. A 1955 , 68 , 1113 . [30] A. X. Levander , T. Tong , K. M. Yu , J. Suh , D. Fu , R. Zhang , H. Lu ,

W. J. Schaff , O. Dubon , W. Walukiewicz , D. G. Cahill , J. Wu , Appl. Phys. Lett. 2011 , 98 , 012108 .

[31] J. Wu , W. Walukiewicz , K. M. Yu , W. Shan , J. W. Ager , E. E. Haller , H. Lu , W. J. Schaff , W. K. Metzger , S. Kurtz , J. Appl. Phys. 2003 , 94 , 6477 .

[32] V. N. Brudnyi , N. G. Kolin , A. I. Potapov , Semiconductors 2003 , 37 , 390 .

[33] I. Chowdhury , R. Prasher , K. Lofgreen , G. Chrysler , S. Narasimhan , R. Mahajan , D. Koester , R. Alley , R. Venkatasubramanian , Nat. Nanotechnol. 2009 , 4 , 235 .

[34] N. E. Coates , S. K. Yee , B. McCulloch , K. C. See , A. Majumdar , R. A. Segalman , J. J. Urban , Adv. Mater. 2013 , 25 , 1629 .

[35] T. Borca-Tasciuc , A. R. Kumar , G. Chen , Rev. Sci. Instrum. 2001 , 72 , 2139 .

Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2015.

Supporting Information

for Adv. Mater., DOI: 10.1002/adma.201501350

Simultaneous Enhancement of Electrical Conductivity andThermopower of Bi2Te3 by Multifunctionality of NativeDefects

Joonki Suh, Kin Man Yu, Deyi Fu, Xinyu Liu, Fan Yang, JinFan, David J. Smith, Yong-Hang Zhang, Jacek K. Furdyna,Chris Dames, Wladyslaw Walukiewicz, and Junqiao Wu*

1

Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2014.

Supporting Information Simultaneous Enhancement of Electrical Conductivity and Thermopower of Bi2Te3 by Multi-Functionality of Native Defects Joonki Suh, Kin Man Yu, Deyi Fu, Xinyu Liu, Fan Yang, Jin Fan, David J. Smith, Yong-Hang Zhang, Jacek K. Furdyna, Chris Dames, Wladyslaw Walukiewicz, and Junqiao Wu*

1. Low-temperature mobility.

Figure S1. Low-temperature mobility of Bi2Te3 film. Comparison of carrier mobility determined at

77 K and 300 K for a 740 nm film as a function of irradiation dose. The mobility in the pristine film

(740 nm thick) at 77 K is nearly two orders of magnitude higher than at 300 K. This difference

becomes much smaller upon irradiation, suggesting that electrically active NDs (donors and

compensated acceptors), as opposed to acoustic phonons, become the dominant scattering centers,

which also increases the Seebeck coefficient. This supports the explanation in the main text of the

2

simultaneous enhancements in both and . Inset shows the depth distribution of the irradiation

He2+ ions in the Bi2Te3 film and GaAs substrate determined by SRIM simulation.

2. Thermopower calculation.

The definition of Seebeck coefficient (thermopower), , can be derived from the solution to the

steady-state Boltzmann transport equation under the relaxation time approximation as[1]

2e

d 3k

2 3 k vkv

k

T

df 0

d

, (S1)

where 2e2 d 3k

2 3 k vkv

k

df 0

d

and k F e . Here e is the elementary

charge, vk

is the electron group velocity, F is Fermi energy, is electric potential and f(0) is the

Fermi-Dirac carrier distribution function. The dependence of relaxation time τ on electron energy E

follows τ((k)) ~ (k) r , where the exponent r = −1/2 accounts for phonon dominated scattering

mechanism, while r = 3/2 accounts for impurity dominated scattering mechanism. To calculate

Seebeck coefficient as a function of carrier concentration, the Fermi level needs to be determined

first based on the charge neutral condition, i.e.

Nd n ,F p ,F 0, (S2)

where Nd is the constant concentration of donors, n and p are the carrier population of the

conduction and valence bands respectively. Setting the conduction band edge as the energy

reference point, i.e. 0 , n can be calculated as

n F d1 exp F kBT , (S3)

where ρ() is the density of states for the conduction band. Here full Fermi-Dirac carrier statistics

are used such that the calculation is valid across all concentrations ranging from non-degenerate to

3

degenerate. Free hole concentration can be calculated in a similar way. In the degenerate doping

limit, Equation (S1) can be simplified to Equation (3) shown in the main text.

3. Characteristics of native defects as charge scattering centers.

Both native defects (NDs) and extrinsic chemical dopants enhance electrical conductivity of Bi2Te3

by donating more charge carriers. While they both behave as charged scattering centers, their

degree of ionized impurity scattering can be significantly different (hence different effects on

Seebeck coefficient).

First, the scattering cross-section is much larger for NDs. For ionized impurity scattering, it is

known that the cross-section is proportional to Z2 as below:

~1

40

Ze2

12 m 2

2

, (S4)

where Z is the charge of the ionized defect center. It is widely known that NDs in semiconductors

have multiple charge states depending on their Fermi level, and this also holds true for Bi2Te3

according to a recent computational investigation in Ref [16]. For instance, Te vacancies have the

charge state of 2+. Recalling that high-energy particle irradiation normally generates Frenkel pairs

(vacancy-interstitial), irradiation-induced NDs can have 4 times larger scattering cross-section

compared to that of single charged extrinsic dopants such as iodine (n-type) and antimony (p-type).

Secondly, irradiation-induced NDs provide more charge scattering centers than chemical doping

even when they donate the same number of free carriers. This is based on the fact that irradiation

produces random damage consisting of donors and compensating acceptors. Although donor-like

NDs (e.g., Te vacancies) are dominant, however acceptors (e.g., Bi vacancies) are also

simultaneously generated as shown in Figure 1d. Both types of NDs naturally act as charge

scattering centers. The carrier scattering rate is given by 1 / N where N is the concentration

of ionized scattering centers. In compensated semiconductors,

4

N n

Z

11

, (S5)

where n is free carrier concentration and θ is the effective compensation ratio. For irradiated Bi2Te3,

θ is estimated to be ~ 0.67 from our SRIM simulation, so N will be ~ 2.5 n. On the contrary, the

uncompensated Bi2Te3 (e.g., I-doped Bi2Te3) will have N ~ n. Therefore, our finding of

simultaneous enhancements in electrical conductivity and thermopower has never been observed in

chemically doped Bi2Te3, in which the conventional wisdom of thermoelectrics governs.

4. Stability of the effects.

Figure S2. Carrier concentration of irradiated Bi2Te3 across a practical temperature range. The

carrier concentration of 740 nm thin-film was measured during heating (red) and cooling (blue)

with a ramping rate of 10 K/min. At each temperature point, the time spent on waiting for

temperature stabilization and the Hall measurement is about 10 minutes, such that the total time of a

full cycle is about 90 minutes.

5. Reduction of cross-plane thermal conductivity in irradiated Bi2Te3.

Figure S3a illustrates these two 3ω samples, namely, “sample” (with Bi2Te3 film) and “reference”

(without Bi2Te3 film). Figure S3b shows the amplitude of the temperature oscillation in the pristine

Bi2Te3 sample (ΔTsample) and reference substrate (ΔTreference), calculated using

5

T 2RdT

dR

V3

V1

, (S6)

where R, V1ω, V3ω are the electrical resistance, 1ω voltage, and 3ω voltage of the gold heater,

respectively, and dR/RdT is the temperature coefficient of resistance of the heater. The average

temperature drop across Bi2Te3 film (ΔTfilm) was determined using ΔTfilm = ΔTsample - ΔTreference, and

the cross-plane thermal conductivity of film (κfilm,) was calculated as

film, Pd

LwTfilm, (S7)

where P is the amplitude of the heater power, d is the thickness of film, and L and w are the length

and width of the heater, respectively. The representative temperature rise to determine κfilm, at

1.5×1015 cm-2 irradiation is shown in Figure S3b. Thermal conductivity was monitored by

irradiating both the sample and reference substrate with the same dose. The R(T) curve of every

sample and reference was re-calibrated after every additional dosing step. We also note that due to

the finite projected range of the alpha particles (see inset of Figure 2a in the main text), the damage

profile in the GaAs substrate will be slightly shallower in the “sample” as compared to the

“reference” measurements. However, the following estimate shows that this effect should contribute

only around 1% of additional uncertainty to the thermal conductivity of the film, and thus is simply

neglected. The damaged region of GaAs can be approximated as a layer 1 m thick that is either ~7

m (sample) or ~8 m (reference) below the top GaAs surface. For a comparable point-defect

concentration of ~1019 cm-3, the thermal conductivity of the damaged GaAs can be estimated as 40

W/mK, as compared to 60 W/mK for pristine GaAs. As a conservative estimate of the additional

difference between these two samples, we estimate the difference between one-dimensional

conduction resistances of 1 m of damaged and undamaged GaAs, and compare it to the thermal

resistance of the 740 nm film at 1 W/mK. On an area normalized basis this is 8.310-9 m2 K/W

compared to 7.4x10-7 m2K/W, or only 1.1%.

6

Figure S3. Thermal conductivity of Bi2Te3 film. (a) Schematic drawings of two types of specimen

used for the differential 3ω measurement: “sample” and “reference”. The only difference is the

additional Bi2Te3 layer in the “sample”. Determined temperature rise in the “sample” and

“reference” (b) before and (c) after irradiation at a dose of 1.5 × 1015 cm-2. Arrows indicate the

temperature rise across the 740 nm Bi2Te3 film (ΔTfilm).

6. Phonon mean free path of Bi2Te3.

We first consider the range of phonon mean free paths (MFPs) that are important in bulk Bi2Te3

prior to irradiation. The lattice thermal conductivity of a bulk material can be expressed as

bulk 13 Cvbulk d , (S8)

where is the phonon frequency, C is the volumetric specific heat capacity per unit frequency, v is

the group velocity, bulk is the bulk MFP, and each term in the integrand is frequency-dependent.

For simplicity we use a Born-von Karman dispersion relation and average the transverse and

longitudinal polarizations. Due to its low Debye temperature of 165 K,[2] at 300 K Bi2Te3 is well

into the Dulong-Petit regime of constant heat capacity. In bulk Bi2Te3 of comparable doping,[3,4]

bulk at room temperature is dominated by umklapp scattering both in-plane and cross-plane. As a

result, bulk T 1, consistent with umklapp-limited transport and inconsistent with other scattering

7

mechanisms such as boundaries and point defects. Thus, the bulk MFP can be approximated as

bulk1 B 2T

v,[5] where the free parameter B is determined by substituting this bulk MFP into

Equation (S8) and fitting the model to experimental data for the in-plane[3] and cross-plane[4] lattice

thermal conductivities. The resulting values are B// = 4.5810-18 s/K (in-plane) and B=1.1210-17

s/K (cross-plane). The other parameters used in the model are the lattice constants[3] (a// = 0.4383

nm, a = 3.0487 nm) and average sound velocities (vs,// = 2090 m/s, vs, = 2017 m/s).[6]

The resulting accumulation functions[7] for bulk Bi2Te3 at 300 K are shown in Figure S4,

along with typical distribution of grain sizes from ~100 nm to 2 m in the films. The calculation

shows that the additional scattering by 2 m grains would have only a modest impact on thermal

conductivity, since 88% (in-plane) and 92% (cross-plane) of bulk is carried by phonons with MFPs

shorter than 2 m. However, for 100 nm grains, effect of grain boundary scattering would be

substantial, and would impact // more than , since the accumulation function at 100 nm is

smaller in plane (51%) than cross plane (64%). Assuming that the in-plane and cross-plane grain

sizes are similar, this calculation also shows that // should become slightly more isotropic as

grain boundary scattering becomes increasingly important.

Figure S4. (a) AFM image of Bi2Te3 films grown by MBE on a GaAs (001) substrate displaying

grains ranging from 100 nm to 2 m and oriented in the film plane. (b) Calculated thermal

8

conductivity accumulation function of non-irradiated Bi2Te3. The shaded region represents the

range of grain sizes observed in the films.

7. Estimation of bounds of in-plane ZT.

As our measured is cross-plane () in Figure S3c, while the measured and are in-plane (//), a

rigorous evaluation of ZT is not within the scope of this work due to the anisotropic transport. For

bulk crystalline Bi2Te3 at similar carrier concentrations, it is well known that // / 5.0 and

// / 2.0 .[8] Using the Wiedemann-Franz law,[9] the corresponding ratio of phonon thermal

conductivities is //,phonon / ,phonon 1.7 . As compared to this reference data, the // / ratio of

the present film samples will differ due to several effects. First, we note that the range of phonon

mean free paths (MFPs) of the bulk materials is estimated to span from ~10 nm to ~1 m, with the

MFPs longer in-plane than cross-plane by a factor of ~2. Phonon scattering by grain boundaries

affects transport in both directions; but because these grains are textured, //,phonon should be

reduced more than ,phonon due to the longer in-plane MFPs, and it is estimated that about 50% of

the in-plane-propagating phonons are scattered at MFPs comparable to the grain sizes in the films

(see Figure S4b). Similarly, the strong impurity scattering also tends to reduce //,phonon more than

,phonon , as seen in measurements of Bi2Te3[8] and modelling of In4Se3-x.

[10] At the optimal

irradiation dose, the NDs distribute over an average distance of ~5 nm, which is much smaller than

the median phonon MFP. Overall the // / ratio of the 740 nm film should be less than that of

single-crystal limit of 2.0.[8] The resulting in-plane ZT at room temperature is calculated in Figure

S5 for two limiting cases of //. It can be seen that the ZT of the optimally irradiated films is at least

0.7 (using the most conservative value of // / = 2.0), and potentially reaches 1.4 in the isotropic

limit ( // / = 1.0). Both values correspond to an enhancement by a factor of ~ 10 in ZT compared

to the pristine-film values.

9

Figure S5. In-plane ZT of the irradiated film for anisotropy ratios of 1 (anisotropic, or random

polycrystalline limit) and 2 (single-crystal limit), respectively. The real ZT value should be in

between these two scenarios. In both scenarios the maximum ZT is enhanced approximately by an

order of magnitude compared to the pristine film.

[1] J. Cai, G. Mahan, Phys. Rev. B 2006, 74, 075201.

[2] O. Madelung, Semiconductors: Data Handbook, Springer, 2004.

[3] C. B. Satterthwaite, R. W. Ure, Phys. Rev. 1957, 108, 1164.

[4] H. J, Goldsmid, Proc. Phys. Soc. Sec. B 1956, 69, 203.

[5] F, Yang, T. Ikeda, G. J. Snyder, C. Dames, J. Appl. Phys. 2010, 108, 034310.

[6] J. O. Jenkins, J. A. Rayne, R. W. Ure, Phys. Rev. B 1972, 5, 3171.

[7] F, Yang, C. Dames, Phys. Rev. B 2013, 87, 035437.

[8] H. Scherrer, S. Scherrer, CRC Handbook of Thermoelectrics. (eds. Rowe, D. M.) CRC Press,

1995.

[9] H. J. Goldsmid, Proc. Phys. Soc. 1958, 72, 17.

[10] H. S. Ji, H. Kim, C. Lee, J.-S. Rhyee, M. H. Kim, M. Kaviany, J. H. Shim, Phys. Rev. B

2013, 87, 125111.